conceptualizing birkhoff’s aesthetic measure using...

Computational Aesthetics in Graphics, Visualization, and Imaging (2007)D. W. Cunningham, G. Meyer, L. Neumann (Editors)

Conceptualizing Birkhoff’s Aesthetic Measure UsingShannon Entropy and Kolmogorov Complexity

Jaume Rigau, Miquel Feixas, and Mateu Sbert

Institut d’Informàtica i Aplicacions, University of Girona, Spain

AbstractIn 1928, George D. Birkhoff introduced the Aesthetic Measure, defined as the ratio between order and complexity,and, in 1965, Max Bense analyzed Birkhoff’s measure from an information theory point of view. In this paper, theconcepts of order and complexity in an image (in our case, a painting) are analyzed in the light of Shannon entropyand Kolmogorov complexity. We also present a new vision of the creative process: the initial uncertainty, obtainedfrom the Shannon entropy of the repertoire (palette), is transformed into algorithmic information content, definedby the Kolmogorov complexity of the image. From this perspective, the Birkhoff’s Aesthetic Measure is presentedas the ratio between the algorithmic reduction of uncertainty (order) and the initial uncertainty (complexity). Themeasures proposed are applied to several works of Mondrian, Pollock, and van Gogh.

Categories and Subject Descriptors (according to ACM CCS): I.4 [Computing Methodologies]: Image Processingand Computer Vision J.5 [Computer Applications]: Arts and Humanities

1. Introduction

From Birkhoff’s aesthetic measure [Bir33], Moles [Mol68]and Bense [Ben69] developed the information aestheticstheory, based on information theory. The concepts of or-der and complexity were formalized from the notion of in-formation provided by Shannon’s work [CT91]. Scha andBod [SB93] stated that in spite of the simplicity of thesebeauty measures, “if we integrate them with other ideas fromperceptual psychology and computational linguistics, theymay in fact constitute a starting point for the development ofmore adequate formal models”.

In this paper, we present a new version of Birkhoff’s mea-sure based on Zurek’s physical entropy [Zur89]. Zurek’swork permits us to look at the creative process as an evo-lutionary process from the initial uncertainty (Shannon en-tropy) to the final order (Kolmogorov complexity). This ap-proach can be interpreted as a transformation of the ini-tial probability distribution of the palette of colors to thealgorithm which describes the final painting. We also ana-lyze several ratios, obtained from Shannon entropy and Kol-mogorov complexity, applied to the global image and differ-ent decompositions of it.

We will use here zeroth-order measures such as Shannon

entropy of the histogram. This is a first step towards updatingclassical Birkhoff’s measure. A next step could be to usehigher-order measures to handle edges, contrast, and spatialfrequency, well studied in visual perception [Bla93].

This paper is organized as follows. In section 2, the infor-mation theory and Kolmogorov complexity are described.In section 3, origins and related work are reviewed. In sec-tions 4 and 5, global and compositional aesthetic measuresare defined and discussed, respectively. Finally, conclusionsare presented.

2. Information Theory and Kolmogorov Complexity

In this section, some basic notions of information the-ory [CT91] and Kolmogorov complexity [LV97] are re-viewed.

2.1. Information-Theoretic Measures

Information theory deals with the transmission, storage andprocessing of information and is used in fields such asphysics, computer science, statistics, biology, image pro-cessing, learning, etc.

Let X be a finite set, let X be a random variable taking

c© The Eurographics Association 2007.

J. Rigau, M. Feixas, and M. Sbert / Conceptualizing Birkhoff’s Aesthetic Measure

values x in X with distribution p(x) = Pr[X = x]. Likewise,let Y be a random variable taking values y inY . The Shannonentropy H(X) of a random variable X is defined by

H(X) =− ∑x∈X

p(x) log p(x). (1)

The Shannon entropy H(X) measures the average uncer-tainty of random variable X . If the logarithms are taken inbase 2, entropy is expressed in bits. The conditional entropyis defined by

H(X |Y ) =− ∑x∈X ,y∈Y

p(x,y) log p(x|y), (2)

where p(x,y) = Pr[X = x,Y = y] is the joint probabilityand p(x|y) = Pr[X = x|Y = y] is the conditional probabil-ity. The conditional entropy H(X |Y ) measures the averageuncertainty associated with X if we know the outcome of Y .The mutual information between X and Y is defined by

I(X ,Y ) = H(X)−H(X |Y ) = H(Y )−H(Y |X) (3)

and represents the shared information between X and Y .

A fundamental result of information theory is the Shannonsource coding theorem, which deals with the encoding of anobject in order to store or transmit it efficiently. The theoremexpresses that the minimal length of an optimal code (forinstance, a Huffman code) fulfills

H(X)≤ ` < H(X)+1, (4)

where ` is the expected length of the optimal binary code forX .

The data processing inequality plays a fundamental rolein many information-theoretic applications: if X → Y → Zis a Markov chain (i.e., p(x,y,z) = p(x)p(y|x)p(z|y)), then

I(X ,Y )≥ I(X ,Z). (5)

This inequality demonstrates that no processing of Y , de-terministic or random, can increase the information that Ycontains about X .

2.2. Kolmogorov Complexity and the Similarity Metric

The Kolmogorov complexity K(x) of a string x is the lengthof the shortest program to compute x on an appropriate uni-versal computer. Essentially, the Kolmogorov complexity ofa string is the length of the ultimate compressed version ofthe string. The conditional complexity K(x|y) of x relative toy is defined as the length of the shortest program to computex given y as an auxiliary input to the computation. The jointcomplexity K(x,y) represents the length of the shortest pro-gram for the pair (x,y) [LV97]. The Kolmogorov complexityis also called algorithmic information and algorithmic ran-domness.

The information distance [BGL∗98] is defined as thelength of the shortest program that computes x from y and

y from x. There it was shown that, up to an additive logarith-mic term, the information distance is given by

E(x,y) = max{K(y|x),K(x|y)}. (6)

This measure is a metric. It is interesting to note that longstrings that differ by a tiny part are intuitively closer thanshort strings that differ by the same amount. Hence,the ne-cessity to normalize the information distance arises. Li etal. [LCL∗04] defined a normalized version of E(x,y), calledthe normalized information distance or the similarity metric:

NID(x,y) =max{K(x|y),K(y|x)}

max{K(x),K(y)}

=K(x,y)−min{K(x),K(y)}

max{K(x),K(y)} . (7)

In addition, they shown that NID is a metric and takes val-ues in [0,1]. It is universal in the sense that if two stringsare similar according to the particular feature described bya particular normalized admissible distance (not necessarilymetric), then they are also similar in the sense of the normal-ized information metric.

Due to the non-computability of Kolmogorov complexity,a feasible version of NID (7), called normalized compressiondistance, is defined as

NCD(x,y) =C(x,y)−min{C(x),C(y)}

max{C(x),C(y)} , (8)

where C(x) and C(y) represent the length of compressedstring x and y, respectively, and C(x,y) the length of the com-pressed pair (x,y). Therefore, NCD approximates NID byusing a standard real-world compressor.

2.3. Physical Entropy

Looking at a system from an observer’s angle, Zurek [Zur89]defined its physical entropy as the sum of the missing infor-mation (Shannon entropy (1)) and the algorithmic informa-tion content (Kolmogorov complexity) of the available data:

Sd = H(Xd)+K(d), (9)

where d is the observed data of the system, K(d) is theKolmogorov complexity of d, and H(Xd) is the conditionalShannon entropy or our ignorance about the system givend [Zur89, LV97].

Physical entropy reflects the fact that measurements canincrease our knowledge about a system. In the beginning, wehave no knowledge about the state of the system, thereforethe physical entropy reduces to the Shannon entropy, reflect-ing our total ignorance. If the system is in a regular state,physical entropy can decrease with the more measurementswe make. In this case, we increase our knowledge about thesystem and we may be able to compress the data efficiently.If the state is not regular, then we cannot achieve compres-sion and the physical entropy remains high [LV97].



3. Origins and Related Work

In 1928, Birkhoff formalized the notion of beauty by the in-troduction of the aesthetic measure, defined as the ratio be-tween order and complexity [Bir33], where “the complexityis roughly the number of elements that the image consistsof and the order is a measure for the number of regularitiesfound in the image” [SB93]. According to Birkhoff, the aes-thetic experience is based on three successive phases:

1. A preliminary effort of attention, which is necessary forthe act of perception, and that increases proportionally tothe complexity (C) of the object.

2. The feeling of value or aesthetic measure (M) that re-wards this effort.

3. The verification that the object is characterized by cer-tain harmony, symmetry or order (O), which seems to benecessary for the aesthetic effect.

From this analysis of the aesthetic experience, Birkhoffsuggested that the aesthetic feelings stem from the harmo-nious interrelations inside the object and that the aestheticmeasure is determined by the order relations in the aestheticobject. As we will see below, different versions of the aes-thetic measure try to capture mainly the order in the object,while the complexity fundamentally plays a normalizationrole.

On the other hand, it is not realistic to expect that amathematical theory would be able to explain the complexi-ties of the aesthetic experience [SB93]. Birkhoff recognizedthe impossibility of comparing objects of different classesand accepted that the aesthetic experience depends on eachobserver. Hence, he proposed to restrict the group of ob-servers and to only apply the measure to similar objects.Excellent overviews of the history of the aesthetic mea-sures can be found in the reports of Greenfield [Gre05] andHoenig [Hoe05] which were presented in the first Workshopon Computational Aesthetics. From this point on, this paperwill focus on the informational aesthetics perspective.

Using information theory, Bense [Ben69] transformedBirkhoff’s measure into an informational measure: redun-dancy divided by statistical information (entropy). Accord-ing to Bense, in any artistic process of creation, we have adetermined repertoire of elements (such as a palette of col-ors, sounds, phonemes, etc.) which is transmitted to the finalproduct. The creative process is a selective process (i.e, tocreate is to select). For instance, if the repertoire is givenby a palette of colors with a probability distribution, the fi-nal product (a painting) is a selection (a realization) of thispalette on a canvas. In general, in an artistic process, or-der is produced from disorder. The distribution of elementsof an aesthetic state has a certain order and the repertoireshows a certain complexity. Bense also distinguished be-tween a global complexity, formed by partial complexities,and a global order, formed by partial orders. His contempo-rary Moles [Mol68] considered order expressed not only asredundancy but also as the degree of predictability.

Nake [Nak05], one of the pioneers of the computer oralgorithmic art (i.e., art explicitly generated by an algo-rithm), considers a painting as a hierarchy of signs, where ateach level of the hierarchy the statistical information contentcould be determined. He conceived the computer as a Uni-versal Picture Generator capable of “creating every possiblepicture out of a combination of available picture elementsand colors” [Nak74].

Different authors have introduced several measureswith the purpose of quantifying aesthetics. Koshelev etal. [KKY98] consider that the running time t(p) of a pro-gram p which generates a given design is a formalizationof Birkhoff’s complexity C, and a monotonically decreasingfunction of the length of the program l(p) (i.e., Kolmogorovcomplexity) represents Birkhoff’s order O. Thus, looking forthe most attractive design, the aesthetic measure is definedby M = 2−l(p)/t(p). For each possible design, they defineits “beauty” as the smallest possible value of the productt(p)2l(p) for all possible programs that generate this design.Machado and Cardoso [MC98] established that an aestheticvisual measure depends on the ratio between image complex-ity and processing complexity. Both are estimated using real-world compressors (jpg and fractal, respectively). They con-sider that images that are simultaneously visually complexand easy to process are the images that have a higher aes-thetic value. Svangård and Nordin [SN04] use the universalsimilarity metric (7) to predict how interesting new imageswill be to the observer, based on a library of aesthetic im-ages. To compute this measure, they also use a combinationof different compressors (8).

4. Global Aesthetic Measures

Next, we present a set of measures to implement, from aninformational perspective, the Birkhoff’s aesthetic measureapplied to an image. We distinguish two kinds of measures:the global ones (Sec. 4) and the compositional ones (Sec. 5).

For a given color image I of N pixels, we use an sRGBcolor representation (i.e., a tristimulus color system) and analphabet A of 256 symbols (8 bits of information) for chan-nel (i.e., 24 bits per pixel). The luminance Y709 (0..255) willbe also used as a representative value of a pixel (it is a per-ceptual function of the importance of the pixel color). Theprobability distributions of the random variables Xr, Xg, Xb,and X` are obtained from the normalization of the intensityhistogram of the corresponding channel (R, G, B, and lumi-nance, respectively). The maximum entropy or uncertaintyfor these random variables is H = log |A|= 8. Thus, the fol-lowing properties are fulfilled:

• 0≤ H(Xr),H(Xg),H(Xb)≤ H• 0≤ H(X`)≤ H• 0≤ Hrgb ≤ log |A|3 = 3H = Hrgb,

where Hrgb = H(Xr)+H(Xg)+H(Xb) is an upper bound ofthe joint entropy H(Xr,Xg,Xb).



Throughout this paper, the following notions are used:

• Repertoire: palette of colors. We assume that is given bythe normalized histogram of the luminance values of theimage (X`) or the respective normalized histograms of theRGB values (Xr, Xg, and Xb).

• Hp: entropy of the repertoire or uncertainty of a pixel.• NHp: uncertainty or information content of an image.• K: Kolmogorov complexity of an image. The use of this

measure implies to take into account an additional con-stant (see [LV97]).

The measures presented will be applied to the set of paint-ings shown in Fig. 1. Their sizes are given in Table 1, wherewe have also indicated the size and rate of compressionachieved by two real-world compressors: jpg and png. Weselect these two compressors as representative examples oflossy and lossless compression, respectively. The jpg com-pressor will be used with maximum quality.

4.1. Shannon Perspective

As we have seen in Sec. 3, the redundancy was proposed byBense and Moles to measure the order in an aesthetic object.For an image, the absolute redundancy H−Hp expresses thereduction of uncertainty due to the choice of a given reper-toire instead of taking a uniform palette. The relative redun-dancy is given by

MH =H−Hp

H. (10)

From a coding perspective, this measure represents the gainobtained using an optimal code to compress the image (4).It expresses one aspect of the creative process: the reductionof uncertainty due to the choice of a palette.

Table 2 shows MH for the set of paintings in Fig. 1, wherethe entropy of a pixel has been computed using the lumi-nance (Hp ≡ H(X`)). We can observe, as expected, how ahigh redundancy is reflected in Mondrian’s paintings whilelow values appear in the Pollock and van Gogh ones. Notethat the MH value for Pollock-2 stands out due to a morehomogeneous repertoire than the other two Pollock’s paint-ings.

4.2. Kolmogorov Perspective

From a Kolmogorov complexity perspective, the order inan image can be measured by the normalized difference be-tween the image size obtained using a constant code for eachcolor (i.e., the maximum size of the image) and the Kol-mogorov complexity of the image:

MK =NHrgb−K

NHrgb. (11)

Due to the non-computability of K, real-world compressorsare used to estimate it. The complementary of this measurecorresponds to the compression ratio. It is an adimensional

value in [0,1] that expresses the degree of order of the imagewithout any a priori knowledge on the palette (the higherthe order of the image, the higher the compression ratio). Inpractice, this measure could be negative due to the presenceof an additive compression constant.

In Table 2, MK has been calculated for the set of paint-ings using the jpg and png compressors. Note that the useof MK alters the ranking obtained by MH . The compressorstake advantage of the degree of order in an image, being de-tected and used in different ways within the process of com-pression. A radical case corresponds to Pollock-2, thatswitches from the lowest position for jpg to the fourth onefor png. This could be due to the fact that, being jpg a lossycompressor, it can more easily detect regular patterns.

4.3. Zurek Perspective

Using the concept of physical entropy (9), we propose a newaesthetic measure given by the ratio between the reduction ofuncertainty (due to the compression achieved) and the initialinformation content of the image:

MS =NHp−K

NHp. (12)

This ratio quantifies the degree of order created from a givenpalette. It is an adimensional value in [0,1], but in practice itcould be negative, similarly to the MK case.

In Table 2, values MS have been computed using the jpgand png compressors. We have considered Hp ≡Hrgb for co-herence with the compressors that use the knowledge of allthe channels. In our experiments, Mondrian’s and Pollock’spaintings correspond to the highest and lowest values in thepng case, respectively. The values near zero in the Pollock’spaintings denote their high randomness. In the jpg case, theordering of some paintings has changed due to the highercapacity of jpg of detecting patterns. For instance, this ex-plains that the value of vanGogh-3 is lower than the valueof Pollock-1.

The plots shown in Fig. 2 express, for three paintings, theevolution of the physical entropy as we make more and moremeasurements. To do this, the content of each painting isprogressively discovered (by columns from left to right), re-ducing the missing information (Shannon entropy) and com-pressing the discovered one (Kolmogorov complexity). Ob-serve the higher compression obtained with jpg (lossy) com-pressor compared with png (lossless) one. As we expected,Mondrian’s paintings show a greater order than van Gogh’sand Pollock’s ones.

5. Compositional Aesthetic Measures

In this section, we analyze the behavior of two new imple-mentations of Birkhoff’s measure using different decompo-sitions of an image.



(a.1) Composition with RedPiet Mondrian, 1938-1939

(a.2) Composition with Red, Blue,Black, Yellow, and Gray

Piet Mondrian, 1921

(a.3) Composition with Gray andLight Brown

Piet Mondrian, 1918

(b.1) Number 1Jackson Pollock, 1950

(b.2) Shimmering SubstanceJackson Pollock, 1946

(b.3) Number 8 (detail)Jackson Pollock, 1949

(c.1) The Starry NightVincent van Gogh, 1889

(c.2) Olive Trees with the Alpillesin the Background

Vincent van Gogh, 1889

(c.3) Wheat Field UnderThreatening Skies

Vincent van Gogh, 1890

Figure 1: Set of paintings.

Image jpg pngFig. Painting Pixels Size Size Ratio Size Rate

1.(a.1) Mondrian-1 316888 951862 160557 0.169 290073 0.3051.(a.2) Mondrian-2 139050 417654 41539 0.100 123193 0.2951.(a.3) Mondrian-3 817740 2453274 855074 0.349 1830941 0.7461.(b.1) Pollock-1 766976 2300982 1049561 0.456 2255842 0.9801.(b.2) Pollock-2 869010 2609178 1377137 0.528 2355263 0.9031.(b.3) Pollock-3 899300 2699654 1286395 0.477 2596686 0.9621.(c.1) vanGogh-1 831416 2495126 919913 0.369 2370415 0.9501.(c.2) vanGogh-2 836991 2511850 862274 0.343 2320454 0.9241.(c.3) vanGogh-3 856449 2570034 1203527 0.468 2402468 0.935

Table 1: Data for paintings in Fig. 1. The sizes (bytes) for their original and compressed files (jpg and png) are shown. Therespective compression ratios achieved are also indicated.



Image Shannon jpg pngCode H(X`) H(Xr) H(Xg) H(Xb) MH MK MS MK MS

Mondrian-1 5.069 5.154 5.072 5.194 0.366 0.831 0.737 0.695 0.525Mondrian-2 6.461 6.330 6.514 6.554 0.192 0.900 0.877 0.705 0.635Mondrian-3 7.328 7.129 7.343 6.421 0.084 0.651 0.600 0.254 0.143Pollock-1 7.874 7.891 7.869 7.801 0.016 0.544 0.535 0.020 0.001Pollock-2 7.091 6.115 7.133 7.528 0.114 0.472 0.390 0.097 -0.044Pollock-3 7.830 7.305 7.866 7.597 0.021 0.523 0.497 0.038 -0.015vanGogh-1 7.858 7.628 7.896 7.712 0.018 0.631 0.619 0.050 0.018vanGogh-2 7.787 7.878 7.766 7.671 0.027 0.657 0.647 0.076 0.049vanGogh-3 7.634 7.901 7.670 7.044 0.046 0.532 0.503 0.065 0.008

Table 2: Aesthetic measures (MH , MK , and MS) for the paintings in Fig. 1 with their respective entropies.

(a) Mondrian-1

(b) Pollock-1

(c) vanGogh-1

Figure 2: Evolution of the physical entropy (missing infor-mation + Kolmogorov complexity) for three paintings shownin Fig. 1.

5.1. Shannon Perspective

From a Shannon perspective, we present here an implemen-tation of the aesthetic measure based on the degree of ordercaptured by a determined decomposition of the image.

To analyze the order of an image, we use a partitioningalgorithm based on mutual information [RFS04]. Given animage with N pixels and an intensity histogram with ni pix-els in bin i, we define a discrete information channel whereinput X represents the bins of the histogram, with probabil-ity distribution {pi} = { ni

N }, and output Y the pixel-to-pixelimage partition, with uniform distribution {q j}= { 1

N }. Theconditional probability {p j|i} of the channel is the transi-tion probability from bin i of the histogram to pixel j of theimage. This information channel is represented by

{pi} X{p j|i}−→ Y {q j} (13)

To partition the image, a greedy strategy which splits theimage in quasi-homogeneous regions is adopted. The proce-dure takes the full image as the unique initial partition andprogressively subdivides it, in a binary space partition (BSP)or quad-tree, chosen according to the maximum mutual in-formation gain for each partitioning step. The algorithm gen-erates a partitioning tree T (I) for a given ratio of mutual in-formation gain or a predefined number of regions (i.e, leavesof the tree, L(T (I))).

This process can also be visualized from

H(X) = I(X ,Y )+H(X |Y ) = I(X ,Y )+ ∑i∈L(T (I))

piHi(Xi),

(14)where pi and Hi(Xi) correspond, respectively, to the areafraction of region i and the entropy of its normalized his-togram. The acquisition of information increases I(X ,Y ) (5)and decreases H(X |Y ), producing a reduction of uncertaintydue to the equalization of the regions. Observe that the max-imum mutual information that can be achieved is H(X).

We consider that the resulting tree captures the struc-ture and hierarchy of the image, and the mutual information



Figure 3: Evolution of ratio MI for the set of paintings inFig. 1.

gained in this decomposition process quantifies the degree oforder from an informational perspective. In other words, themutual information of this channel measures the capacity ofan image to be ordered or the feasibility of decomposing itby an observer.

Similarly to Bense’s communication channel between therepertoire and the final product, the channel (13) can beseen as the information (or communication) channel that ex-presses the selection of colors on a canvas. Hence, given aninitial entropy or uncertainty of the image, the evolution ofthe ratio I(X ,Y )/H(X), represents this selection process:

MI(r) =I(X`,Yr)H(X`)

, (15)

where r is the resolution level (i.e., number of regions de-sired or, equivalently, number of leaves in the tree), X ≡ X`,and Yr is the random variable defined from the area distribu-tion. It is an adimensional ratio in [0,1].

In Fig. 3 we show the evolution of MI for the set ofpaintings. Observe that the capacity of extracting order fromeach painting coincides with the behavior expected by anobserver. Note the grouping of the three different paintingstyles (plots of Pollock-1 and Pollock-2 are over-lapped). In Fig. 4, the resulting partitions of three paintingsare shown for r = 10.

5.2. Kolmogorov Perspective

The degree of order of an image is now analyzed using a sim-ilarity measure between its different parts. To do this, givena predefined decomposition of the image, we compute theaverage of the normalized information distance (7) betweeneach pair of subimages:

MD(r) = 1− avg1≤i< j≤r{NID(i, j)}, (16)

where r is the number of regions or subimages provided bythe decomposition, and NID(i, j) the distance between thesubimages Ii and I j. This value ranges from 0 to 1 and ex-presses the order inside the image.

(a) Mondrian-2 (b) Pollock-2

(c) vanGogh-2

Figure 4: Decomposition obtained for r = 10 using the par-titioning algorithm based on the maximization of mutual in-formation. The corresponding values MI for each image are0.314, 0.005, and 0.061, respectively.

Image jpg pngCode MD MD

Mondrian-1 0.208 0.104Mondrian-2 0.299 0.099Mondrian-3 0.148 0.038Pollock-1 0.129 0.028Pollock-2 0.123 0.026Pollock-3 0.128 0.023vanGogh-1 0.140 0.021vanGogh-2 0.142 0.020vanGogh-3 0.123 0.022

Table 3: The values MD for the set of paintings in Fig. 1.

In Table 3, the values MD for the set of paintings are cal-culated using a 3×3 regular grid and NCD(i, j) (8) as an ap-proximation of NID(i, j). Note that, like the previous com-positional measure (15), the paintings are classified accord-ing to the author (specially in the png case).

6. Conclusions

In this paper, the concepts of order and complexity in animage have been analyzed using the notions of Shannon en-tropy and Kolmogorov complexity. Different ratios based onthese measures have been studied for different decomposi-tions of the image. A new version of Birkhoff’s aestheticmeasure has also been presented using Zurek’s physical en-tropy. This new measure allowed us to introduce a simpleformalization of the creative process based on the conceptsof uncertainty reduction and information compression.



The analysis presented can be extended in two differentlines. On the one hand, the zeroth order measures used in thispaper can be extended to higher order measures such as en-tropy rate and excess entropy of an image [BFBS06, FC03].These measures can be used to quantify, respectively, the ir-reducible randomness and the degree of structure of an im-age. On the other hand, following Zurek’s work, the artisticprocess can be analyzed from the viewpoint of a Maxwell’sdemon-type artist or observer [Zur89].

Acknowledgments

This report has been funded in part by grant numbers IST-2-004363 (GameTools) of the European Community, andTIN2004-07451-C03-01 of the Ministry of Education andScience (Spanish Government).

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